Heat oil in a large nonstick skillet over medium-high heat. Add chicken and cook 6 to 8 minutes, turning once, until golden-brown and no longer pink at center. Remove to cutting board; cut each breast half in half lengthwise. Place on a warm serving platter; cover loosely with foil to keep warm.

Place water, onion and garlic in same skillet. Cook until onions are soft, about 3 minutes. Add tomatoes, and remaining salt and pepper. Cook until juices released from tomatoes start to boil. Stir in vinegar, then add arugula. Toss with tongs or 2 large spoons until well mixed. Pour over chicken. Scatter cheese over the top.

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